Go ahead and load the desmos calculator: https://www.desmos.com/calculator
Now graph $x^x$
You should see something like this. An apparent continuation of the curve is shown.
Upon zooming in, it vanishes! What is causing Desmos to be haunted by ghosts?
On
See this video which gives an explanation. The reason there is that for negative $x$ such that $x \geq -1$ and $\frac{1}{x}$ is even $x^x$ is imaginary.
The root issue is that the notation $x^x$ does not represent a well-defined real-valued function when $x\leq 0$.
Probably the most sensible continuation to negative numbers is via restriction of the complex function $F(x) = \exp(x \log x)$ to the real line. Of course $\log(x)$ is multi-valued so you could take e.g. the principal value. But this produces non-real results for some rational values of $x$ where one might "expect" a real result, i.e. $F(-1/3)$ is complex and does not equal $-\sqrt[3]{3}.$
What Desmos seems to be doing instead is extending $x^x$ to a real-valued function on the negative rationals with odd denominator (and leaving $f$ undefined at other negative $x$). This explains the sign alternation as well as why the function disappears when you zoom in: if Desmos happens to only sample $f$ at negative points that aren't rational with odd denominator, it won't draw anything because all sampled values are undefined.